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arXiv · 1402.5347

Unconditional Uniqueness of the cubic Gross-Pitaevskii Hierarchy with Low Regularity

Younghun Hong·Kenneth Taliaferro·Zhihui Xie
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Abstract

In this paper, we establish the unconditional uniqueness of solutions to the cubic Gross-Pitaevskii hierarchy on $\mathbb{R}^d$ in a low regularity Sobolev type space. More precisely, we reduce the regularity $s$ down to the currently known regularity requirement for unconditional uniqueness of solutions to the cubic nonlinear Schr\"odinger equation ($s\ge\frac{d}{6}$ if $d=1,2$ and $s>s_c=\frac{d-2}{2}$ if $d\ge 3$). In such a way, we extend the recent work of Chen-Hainzl-Pavlovi\'c-Seiringer.

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Younghun Hong, Kenneth Taliaferro, Zhihui Xie. 2014-02-21. Unconditional Uniqueness of the cubic Gross-Pitaevskii Hierarchy with Low Regularity. https://arxiv.org/abs/1402.5347

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